Geodesic
On varieties of Leibniz--Poisson algebras with the identity $\{x,y\}\cdot \{z,t\}=0$
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 1, pp. 97-104

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Let $K$ be an arbitrary field and let $A$ be a $K$-algebra. The polynomial identities satisfied by $A$ can be measured through the asymptotic behavior of the sequence of codimensions of $A$. We study varieties of Leibniz–Poisson algebras, whose ideals of identities contain the identity $\{x,y\}\cdot \{z,t\}=0$, we study an interrelation between such varieties and varieties of Leibniz algebras. We show that from any Leibniz algebra $L$ one can construct the Leibniz–Poisson algebra $A$ and the properties of $L$ are close to the properties of $A$. We show that if the ideal of identities of a Leibniz–Poisson variety $\mathcal V$ does not contain any Leibniz polynomial identity then $\mathcal V$ has overexponential growth of the codimensions. We construct a variety of Leibniz–Poisson algebras with almost exponential growth.
Keywords: variety of algebras, growth of a variety.
Mots-clés : Poisson algebra, Leibniz–Poisson algebra 
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     title = {On varieties of {Leibniz--Poisson} algebras with the identity $\{x,y\}\cdot \{z,t\}=0$},
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Sergey M. Ratseev. On varieties of Leibniz--Poisson algebras with the identity $\{x,y\}\cdot \{z,t\}=0$. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 6 (2013) no. 1, pp. 97-104. http://geodesic.mathdoc.fr/item/JSFU_2013_6_1_a9/